bosaFS analyses LMER
Pascale Caissy
2021-03-11
Préparation des données
Méthode de catégorisation des proies :
Utiliser d’abord la taxonomie pour regrouper ensemble;
Vérifier à la fois l’apport en nombre et en % carbone pour chaque catégorie;
Rassembler dans une autre catégorie quand représente < 1 % du carbone et < 5 % du nombre de proies.
Préparation des données par région d’échantillonnage.
## Using region_year as value column: use value.var to override.
PCA
PCA des régions-années, et relations entre l’environnement et l’abondance de zoo et de larves
Modèles de succès alimentaire
Exploration préliminaire
Concernant les mesures de taille spécifiquement, on utilisera les variables log-transformées.
On fera de même avec la mesure de succès alimentaire (feeding_success).
## 2009 2010 2011 2014 2015
## Amundsen Gulf Mouth NA NA NA NA 32.85720
## Coronation Maud NA NA 15.59700 NA NA
## Lancaster Sound NA 13.23085 13.62750 NA 16.59357
## Larsen Sound - Victoria Strait NA 11.30658 NA NA NA
## Mackenzie Shelf 12.6857 27.09488 NA 35.40000 31.54290
## NEG NA NA NA NA NA
## North Water NA NA NA 17.73251 NA
## Peel Sound NA 10.81823 17.42556 12.13674 11.36489
## West Baffin Bay NA NA NA NA 14.48783
## 2016 2017 2018
## Amundsen Gulf Mouth NA NA NA
## Coronation Maud 22.55682 16.26570 14.98442
## Lancaster Sound 17.96064 15.33450 NA
## Larsen Sound - Victoria Strait 14.74777 NA 11.03090
## Mackenzie Shelf NA NA NA
## NEG NA 19.12333 NA
## North Water 20.41569 NA 21.30636
## Peel Sound 12.85020 NA NA
## West Baffin Bay 11.19310 NA NA
## log_est_standard_length sampling_day open_water_day
## log_est_standard_length 1.00 0.40 0.56
## sampling_day 0.40 1.00 0.23
## open_water_day 0.56 0.23 1.00
## prof_mel -0.01 0.10 -0.01
## surf_sal_kgm3 0.18 -0.16 0.46
## surf_temp_degC 0.47 0.04 0.36
## NASC_zoo 0.28 -0.02 0.46
## prof_mel surf_sal_kgm3 surf_temp_degC NASC_zoo
## log_est_standard_length -0.01 0.18 0.47 0.28
## sampling_day 0.10 -0.16 0.04 -0.02
## open_water_day -0.01 0.46 0.36 0.46
## prof_mel 1.00 0.33 -0.36 -0.04
## surf_sal_kgm3 0.33 1.00 -0.17 0.24
## surf_temp_degC -0.36 -0.17 1.00 0.56
## NASC_zoo -0.04 0.24 0.56 1.00
##
## n= 339
##
##
## P
## log_est_standard_length sampling_day open_water_day
## log_est_standard_length 0.0000 0.0000
## sampling_day 0.0000 0.0000
## open_water_day 0.0000 0.0000
## prof_mel 0.8256 0.0652 0.8615
## surf_sal_kgm3 0.0010 0.0027 0.0000
## surf_temp_degC 0.0000 0.4248 0.0000
## NASC_zoo 0.0000 0.7638 0.0000
## prof_mel surf_sal_kgm3 surf_temp_degC NASC_zoo
## log_est_standard_length 0.8256 0.0010 0.0000 0.0000
## sampling_day 0.0652 0.0027 0.4248 0.7638
## open_water_day 0.8615 0.0000 0.0000 0.0000
## prof_mel 0.0000 0.0000 0.4629
## surf_sal_kgm3 0.0000 0.0017 0.0000
## surf_temp_degC 0.0000 0.0017 0.0000
## NASC_zoo 0.4629 0.0000 0.0000
##
## Pearson's product-moment correlation
##
## data: dfish$log_carbon_mg and dfish$log_est_standard_length
## t = 26.732, df = 337, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.7869183 0.8557199
## sample estimates:
## cor
## 0.8243398
##
## Pearson's product-moment correlation
##
## data: dfish$log_feeding_success and dfish$log_est_standard_length
## t = 4.1572, df = 337, p-value = 4.091e-05
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.1171006 0.3198589
## sample estimates:
## cor
## 0.2208648
##
## Pearson's product-moment correlation
##
## data: dfish$log_feeding_success and dfish$log_carbon_mg
## t = 19.851, df = 337, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.6809144 0.7797242
## sample estimates:
## cor
## 0.734183
##
## Pearson's product-moment correlation
##
## data: dfish$fish_cond and dfish$log_est_standard_length
## t = 0.56943, df = 337, p-value = 0.5694
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.07576528 0.13707059
## sample estimates:
## cor
## 0.0310041
##
## Pearson's product-moment correlation
##
## data: dfish$fish_cond and dfish$log_feeding_success
## t = 3.1815, df = 337, p-value = 0.001601
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.06543369 0.27232831
## sample estimates:
## cor
## 0.1707627
La quantité de carbone ingérée est fortement corrélée à la taille des poissons (R = 0.8243398) !
La corrélation entre la taille des poissons et leur succès alimentaire est significative mais bien plus faible (R = 0.2208648) qu’entre la quantité de carbone ingérée et le succès alimentaire (R = cor(dfish$log_carbon_mg,dfish$log_feeding_success)).
Les plus grands poissons n’ont pas nécessairement une meilleure condition physique; la corrélation entre la condition et la taille n’est pas significative (R = 0.0310041).
La corrélation entre le succès alimentaire (mesure à court terme de l’alimentation des poissons) et la condition (mesure intégratrice de l’alimentation des poissons) des individus est significative mais très bruitée (R = 0.1707627).
Succès alimentaire et environnement
Explorations des données
On utilisera la variable log-transformée log_indstandard qui représente la densité de larves filtrées par les filets corrigé en fonction de la profondeur échantillonnée.
La variable NASC_zoo qui représente la concentration de mesozooplankton observée par méthodes acoustiques est problématique : les très fortes valeurs nuisent à des relations linéaires entre variables. On utilisera les valeurs log-transformées.
## log_feeding_success log_indstandard sampling_day
## log_feeding_success 1.00 -0.10 0.13
## log_indstandard -0.10 1.00 -0.24
## sampling_day 0.13 -0.24 1.00
## open_water_day 0.29 -0.07 0.23
## surf_sal_kgm3 0.20 0.35 -0.16
## surf_temp_degC 0.04 -0.42 0.04
## log_NASC_zoo 0.25 -0.09 -0.10
## open_water_day surf_sal_kgm3 surf_temp_degC log_NASC_zoo
## log_feeding_success 0.29 0.20 0.04 0.25
## log_indstandard -0.07 0.35 -0.42 -0.09
## sampling_day 0.23 -0.16 0.04 -0.10
## open_water_day 1.00 0.46 0.36 0.66
## surf_sal_kgm3 0.46 1.00 -0.17 0.35
## surf_temp_degC 0.36 -0.17 1.00 0.49
## log_NASC_zoo 0.66 0.35 0.49 1.00
##
## n= 339
##
##
## P
## log_feeding_success log_indstandard sampling_day
## log_feeding_success 0.0602 0.0168
## log_indstandard 0.0602 0.0000
## sampling_day 0.0168 0.0000
## open_water_day 0.0000 0.1837 0.0000
## surf_sal_kgm3 0.0002 0.0000 0.0027
## surf_temp_degC 0.4284 0.0000 0.4248
## log_NASC_zoo 0.0000 0.1098 0.0702
## open_water_day surf_sal_kgm3 surf_temp_degC log_NASC_zoo
## log_feeding_success 0.0000 0.0002 0.4284 0.0000
## log_indstandard 0.1837 0.0000 0.0000 0.1098
## sampling_day 0.0000 0.0027 0.4248 0.0702
## open_water_day 0.0000 0.0000 0.0000
## surf_sal_kgm3 0.0000 0.0017 0.0000
## surf_temp_degC 0.0000 0.0017 0.0000
## log_NASC_zoo 0.0000 0.0000 0.0000
Modèles de régression linéaire
On va établir les modèles de régression linéaire multiples pour essayer d’expliquer la variabilité du succès alimentaire des poissons échantillonnés.
Lorsque pertinent, nous utiliserons des modèles à effet mixtes aléatoires pour tenir compte de la forte hétérogénéité spatiale de notre échantillonnage.
## Start: AIC=-533.74
## log_feeding_success ~ 1
##
## Df Sum of Sq RSS AIC
## + open_water_day 1 5.7894 64.012 -561.09
## + log_NASC_zoo 1 4.4340 65.368 -553.98
## + surf_sal_kgm3 1 2.7691 67.033 -545.46
## + log_indstandard 1 0.7288 69.073 -535.29
## <none> 69.802 -533.74
## + surf_temp_degC 1 0.1300 69.672 -532.37
##
## Step: AIC=-561.09
## log_feeding_success ~ open_water_day
##
## Df Sum of Sq RSS AIC
## + log_NASC_zoo 1 0.4661 63.546 -561.57
## + log_indstandard 1 0.4643 63.548 -561.56
## + surf_sal_kgm3 1 0.3906 63.622 -561.16
## <none> 64.012 -561.09
## + surf_temp_degC 1 0.2796 63.733 -560.57
## - open_water_day 1 5.7894 69.802 -533.74
##
## Step: AIC=-561.57
## log_feeding_success ~ open_water_day + log_NASC_zoo
##
## Df Sum of Sq RSS AIC
## + surf_temp_degC 1 0.70654 62.840 -563.36
## + log_indstandard 1 0.41805 63.128 -561.80
## <none> 63.546 -561.57
## + surf_sal_kgm3 1 0.34092 63.205 -561.39
## - log_NASC_zoo 1 0.46611 64.012 -561.09
## - open_water_day 1 1.82156 65.368 -553.98
##
## Step: AIC=-563.36
## log_feeding_success ~ open_water_day + log_NASC_zoo + surf_temp_degC
##
## Df Sum of Sq RSS AIC
## + log_indstandard 1 1.26168 61.578 -568.23
## <none> 62.840 -563.36
## + surf_sal_kgm3 1 0.05008 62.789 -561.63
## - surf_temp_degC 1 0.70654 63.546 -561.57
## - log_NASC_zoo 1 0.89305 63.733 -560.57
## - open_water_day 1 1.91649 64.756 -555.17
##
## Step: AIC=-568.23
## log_feeding_success ~ open_water_day + log_NASC_zoo + surf_temp_degC +
## log_indstandard
##
## Df Sum of Sq RSS AIC
## <none> 61.578 -568.23
## + surf_sal_kgm3 1 0.34054 61.237 -568.11
## - log_NASC_zoo 1 1.15837 62.736 -563.91
## - log_indstandard 1 1.26168 62.840 -563.36
## - surf_temp_degC 1 1.55017 63.128 -561.80
## - open_water_day 1 1.91256 63.490 -559.86## Step Df Deviance Resid. Df Resid. Dev AIC
## 1 NA NA 338 69.80162 -533.7363
## 2 + open_water_day -1 5.7894295 337 64.01219 -561.0881
## 3 + log_NASC_zoo -1 0.4661140 336 63.54607 -561.5656
## 4 + surf_temp_degC -1 0.7065431 335 62.83953 -563.3560
## 5 + log_indstandard -1 1.2616830 334 61.57785 -568.2316##
## Call:
## lm(formula = log_feeding_success ~ open_water_day + log_NASC_zoo +
## surf_temp_degC + log_indstandard, data = dfish)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.65508 -0.23667 0.05148 0.29186 1.06973
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.1732285 0.0610967 -51.938 < 2e-16 ***
## open_water_day 0.0029264 0.0009086 3.221 0.00140 **
## log_NASC_zoo 0.1368568 0.0545987 2.507 0.01266 *
## surf_temp_degC -0.0372677 0.0128523 -2.900 0.00398 **
## log_indstandard -0.0893786 0.0341663 -2.616 0.00930 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4294 on 334 degrees of freedom
## Multiple R-squared: 0.1178, Adjusted R-squared: 0.1073
## F-statistic: 11.15 on 4 and 334 DF, p-value: 1.674e-08## Registered S3 methods overwritten by 'car':
## method from
## influence.merMod lme4
## cooks.distance.influence.merMod lme4
## dfbeta.influence.merMod lme4
## dfbetas.influence.merMod lme4## open_water_day log_NASC_zoo surf_temp_degC log_indstandard
## 1.786072 2.096606 1.633757 1.242500
Les conditions environnementales expliquent mal la variabilité du succès d’alimentation.
Seulement la salinité de surface, l’abondance de larves, l’abondance de macrozooplancton révélée par l’acoustique et le nombre de jours depuis la débâcle des poissons explique < 10 % de la variance observée (\(R^2\) = 0.1072512)
On va maintenant vérifier avec des modèles mixtes l’influence possible de l’hétérogénéité régionale.
## boundary (singular) fit: see ?isSingular## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula:
## log_feeding_success ~ log_indstandard + surf_sal_kgm3 + open_water_day +
## log_NASC_zoo + (log_indstandard + surf_sal_kgm3 + open_water_day +
## log_NASC_zoo | region)
## Data: dfish.LMER
##
## REML criterion at convergence: 340
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.12632 -0.51196 0.06082 0.69590 2.71917
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## region (Intercept) 1.015e-01 0.318632
## log_indstandard 9.381e-02 0.306280 0.62
## surf_sal_kgm3 2.379e-04 0.015423 0.05 0.82
## open_water_day 3.946e-05 0.006281 0.63 1.00 0.80
## log_NASC_zoo 3.610e-01 0.600815 -0.68 -0.99 -0.76 -0.99
## Residual 1.480e-01 0.384661
## Number of obs: 314, groups: region, 7
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -3.665007 0.313906 4.361732 -11.675 0.000187 ***
## log_indstandard -0.136376 0.125375 3.256618 -1.088 0.350586
## surf_sal_kgm3 0.017754 0.011830 8.135434 1.501 0.171186
## open_water_day -0.002020 0.002797 3.049095 -0.722 0.521643
## log_NASC_zoo 0.335765 0.240798 3.404193 1.394 0.247281
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) lg_nds srf__3 opn_w_
## lg_ndstndrd 0.365
## srf_sl_kgm3 -0.749 0.324
## open_wtr_dy 0.316 0.843 0.210
## log_NASC_zo -0.218 -0.896 -0.392 -0.917
## convergence code: 0
## boundary (singular) fit: see ?isSingular## # Intraclass Correlation Coefficient
##
## Adjusted ICC: 0.389
## Conditional ICC: 0.338## boundary (singular) fit: see ?isSingular## Warning: Model failed to converge with 3 negative eigenvalues: -1.4e-02 -1.6e-01
## -1.8e-01## boundary (singular) fit: see ?isSingular
## boundary (singular) fit: see ?isSingular## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.190746 (tol = 0.002, component 1)## ANOVA-like table for random-effects: Single term deletions
##
## Model:
## log_feeding_success ~ log_indstandard + surf_sal_kgm3 + open_water_day + log_NASC_zoo + (log_indstandard + surf_sal_kgm3 + open_water_day + log_NASC_zoo | region)
## npar
## <none> 21
## log_indstandard in (log_indstandard + surf_sal_kgm3 + open_water_day + log_NASC_zoo | region) 16
## surf_sal_kgm3 in (log_indstandard + surf_sal_kgm3 + open_water_day + log_NASC_zoo | region) 16
## open_water_day in (log_indstandard + surf_sal_kgm3 + open_water_day + log_NASC_zoo | region) 16
## log_NASC_zoo in (log_indstandard + surf_sal_kgm3 + open_water_day + log_NASC_zoo | region) 16
## logLik
## <none> -169.98
## log_indstandard in (log_indstandard + surf_sal_kgm3 + open_water_day + log_NASC_zoo | region) -180.11
## surf_sal_kgm3 in (log_indstandard + surf_sal_kgm3 + open_water_day + log_NASC_zoo | region) -169.99
## open_water_day in (log_indstandard + surf_sal_kgm3 + open_water_day + log_NASC_zoo | region) -173.29
## log_NASC_zoo in (log_indstandard + surf_sal_kgm3 + open_water_day + log_NASC_zoo | region) -181.60
## AIC
## <none> 381.97
## log_indstandard in (log_indstandard + surf_sal_kgm3 + open_water_day + log_NASC_zoo | region) 392.22
## surf_sal_kgm3 in (log_indstandard + surf_sal_kgm3 + open_water_day + log_NASC_zoo | region) 371.97
## open_water_day in (log_indstandard + surf_sal_kgm3 + open_water_day + log_NASC_zoo | region) 378.59
## log_NASC_zoo in (log_indstandard + surf_sal_kgm3 + open_water_day + log_NASC_zoo | region) 395.20
## LRT
## <none>
## log_indstandard in (log_indstandard + surf_sal_kgm3 + open_water_day + log_NASC_zoo | region) 20.2518
## surf_sal_kgm3 in (log_indstandard + surf_sal_kgm3 + open_water_day + log_NASC_zoo | region) 0.0055
## open_water_day in (log_indstandard + surf_sal_kgm3 + open_water_day + log_NASC_zoo | region) 6.6182
## log_NASC_zoo in (log_indstandard + surf_sal_kgm3 + open_water_day + log_NASC_zoo | region) 23.2337
## Df
## <none>
## log_indstandard in (log_indstandard + surf_sal_kgm3 + open_water_day + log_NASC_zoo | region) 5
## surf_sal_kgm3 in (log_indstandard + surf_sal_kgm3 + open_water_day + log_NASC_zoo | region) 5
## open_water_day in (log_indstandard + surf_sal_kgm3 + open_water_day + log_NASC_zoo | region) 5
## log_NASC_zoo in (log_indstandard + surf_sal_kgm3 + open_water_day + log_NASC_zoo | region) 5
## Pr(>Chisq)
## <none>
## log_indstandard in (log_indstandard + surf_sal_kgm3 + open_water_day + log_NASC_zoo | region) 0.0011208
## surf_sal_kgm3 in (log_indstandard + surf_sal_kgm3 + open_water_day + log_NASC_zoo | region) 0.9999999
## open_water_day in (log_indstandard + surf_sal_kgm3 + open_water_day + log_NASC_zoo | region) 0.2506148
## log_NASC_zoo in (log_indstandard + surf_sal_kgm3 + open_water_day + log_NASC_zoo | region) 0.0003045
##
## <none>
## log_indstandard in (log_indstandard + surf_sal_kgm3 + open_water_day + log_NASC_zoo | region) **
## surf_sal_kgm3 in (log_indstandard + surf_sal_kgm3 + open_water_day + log_NASC_zoo | region)
## open_water_day in (log_indstandard + surf_sal_kgm3 + open_water_day + log_NASC_zoo | region)
## log_NASC_zoo in (log_indstandard + surf_sal_kgm3 + open_water_day + log_NASC_zoo | region) ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## unable to evaluate scaled gradient## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge: degenerate Hessian with 1 negative eigenvalues## Warning: Model failed to converge with 1 negative eigenvalue: -1.6e+00## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: log_feeding_success ~ open_water_day + surf_sal_kgm3 + log_NASC_zoo +
## log_indstandard + (log_NASC_zoo + log_indstandard | region)
## Data: dfish.LMER
##
## REML criterion at convergence: 347
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.4276 -0.4805 0.0617 0.6869 2.7589
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## region (Intercept) 0.33429 0.5782
## log_NASC_zoo 0.16898 0.4111 -1.00
## log_indstandard 0.03931 0.1983 0.98 -0.98
## Residual 0.15222 0.3902
## Number of obs: 314, groups: region, 7
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -3.671298 0.358515 13.590807 -10.240 9.13e-08 ***
## open_water_day -0.001177 0.001556 7.587228 -0.756 0.4722
## surf_sal_kgm3 0.019656 0.009638 52.037685 2.040 0.0465 *
## log_NASC_zoo 0.220313 0.174097 5.527321 1.265 0.2564
## log_indstandard -0.146969 0.089530 4.097201 -1.642 0.1743
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) opn_w_ srf__3 l_NASC
## open_wtr_dy 0.058
## srf_sl_kgm3 -0.720 -0.276
## log_NASC_zo -0.551 -0.237 -0.039
## lg_ndstndrd 0.691 0.012 -0.072 -0.785
## convergence code: 0
## unable to evaluate scaled gradient
## Model failed to converge: degenerate Hessian with 1 negative eigenvalues## # Intraclass Correlation Coefficient
##
## Adjusted ICC: 0.359
## Conditional ICC: 0.327## Warning in checkMatrixPackageVersion(): Package version inconsistency detected.
## TMB was built with Matrix version 1.3.2
## Current Matrix version is 1.2.18
## Please re-install 'TMB' from source using install.packages('TMB', type = 'source') or ask CRAN for a binary version of 'TMB' matching CRAN's 'Matrix' package## [[1]]## `geom_smooth()` using formula 'y ~ x'
##
## [[2]]
## [[2]]$region## `geom_smooth()` using formula 'y ~ x'
##
##
## [[3]]
##
## [[4]]## `geom_smooth()` using formula 'y ~ x'
Ajouter les régions comme effet aléatoire est plus rigoureux d’un point de vue de l’analyse de nos résultats, et cela permet de tenir compte de la variabilité de l’effet des variables explicatives sur le succès alimentaire selon les régions, en particulier de la densité de zooplancton observée par l’acoustique qui démontre des effets parfois inverses.
Condition et environnement
Explorations des données
## fish_cond log_est_standard_length log_indstandard
## fish_cond 1.00 0.03 -0.22
## log_est_standard_length 0.03 1.00 -0.28
## log_indstandard -0.22 -0.28 1.00
## sampling_day -0.05 0.40 -0.24
## open_water_day 0.15 0.56 -0.07
## surf_sal_kgm3 -0.08 0.18 0.35
## surf_temp_degC 0.16 0.47 -0.42
## log_NASC_zoo -0.03 0.29 -0.09
## sampling_day open_water_day surf_sal_kgm3
## fish_cond -0.05 0.15 -0.08
## log_est_standard_length 0.40 0.56 0.18
## log_indstandard -0.24 -0.07 0.35
## sampling_day 1.00 0.23 -0.16
## open_water_day 0.23 1.00 0.46
## surf_sal_kgm3 -0.16 0.46 1.00
## surf_temp_degC 0.04 0.36 -0.17
## log_NASC_zoo -0.10 0.66 0.35
## surf_temp_degC log_NASC_zoo
## fish_cond 0.16 -0.03
## log_est_standard_length 0.47 0.29
## log_indstandard -0.42 -0.09
## sampling_day 0.04 -0.10
## open_water_day 0.36 0.66
## surf_sal_kgm3 -0.17 0.35
## surf_temp_degC 1.00 0.49
## log_NASC_zoo 0.49 1.00
##
## n= 339
##
##
## P
## fish_cond log_est_standard_length log_indstandard
## fish_cond 0.5694 0.0000
## log_est_standard_length 0.5694 0.0000
## log_indstandard 0.0000 0.0000
## sampling_day 0.3358 0.0000 0.0000
## open_water_day 0.0055 0.0000 0.1837
## surf_sal_kgm3 0.1285 0.0010 0.0000
## surf_temp_degC 0.0029 0.0000 0.0000
## log_NASC_zoo 0.6047 0.0000 0.1098
## sampling_day open_water_day surf_sal_kgm3
## fish_cond 0.3358 0.0055 0.1285
## log_est_standard_length 0.0000 0.0000 0.0010
## log_indstandard 0.0000 0.1837 0.0000
## sampling_day 0.0000 0.0027
## open_water_day 0.0000 0.0000
## surf_sal_kgm3 0.0027 0.0000
## surf_temp_degC 0.4248 0.0000 0.0017
## log_NASC_zoo 0.0702 0.0000 0.0000
## surf_temp_degC log_NASC_zoo
## fish_cond 0.0029 0.6047
## log_est_standard_length 0.0000 0.0000
## log_indstandard 0.0000 0.1098
## sampling_day 0.4248 0.0702
## open_water_day 0.0000 0.0000
## surf_sal_kgm3 0.0017 0.0000
## surf_temp_degC 0.0000
## log_NASC_zoo 0.0000
Modèles de régression linéaire
On va établir les modèles de régression linéaire multiples pour essayer d’expliquer la variabilité de l’indice de condition des poissons échantillonnés.
Lorsque pertinent, nous utiliserons des modèles à effet mixtes aléatoires pour tenir compte de la forte hétérogénéité spatiale de notre échantillonnage.
## Start: AIC=-767.12
## fish_cond ~ 1
##
## Df Sum of Sq RSS AIC
## + log_indstandard 1 1.62212 33.443 -781.18
## + surf_temp_degC 1 0.91285 34.152 -774.06
## + open_water_day 1 0.79454 34.270 -772.89
## + surf_sal_kgm3 1 0.23996 34.825 -767.45
## <none> 35.065 -767.12
## + log_NASC_zoo 1 0.02791 35.037 -765.39
##
## Step: AIC=-781.18
## fish_cond ~ log_indstandard
##
## Df Sum of Sq RSS AIC
## + open_water_day 1 0.64208 32.801 -785.75
## + surf_temp_degC 1 0.21519 33.228 -781.37
## <none> 33.443 -781.18
## + log_NASC_zoo 1 0.07780 33.365 -779.97
## + surf_sal_kgm3 1 0.00235 33.441 -779.20
## - log_indstandard 1 1.62212 35.065 -767.12
##
## Step: AIC=-785.75
## fish_cond ~ log_indstandard + open_water_day
##
## Df Sum of Sq RSS AIC
## + log_NASC_zoo 1 1.15898 31.642 -795.95
## + surf_sal_kgm3 1 0.29708 32.504 -786.83
## <none> 32.801 -785.75
## + surf_temp_degC 1 0.03568 32.765 -784.12
## - open_water_day 1 0.64208 33.443 -781.18
## - log_indstandard 1 1.46965 34.270 -772.89
##
## Step: AIC=-795.95
## fish_cond ~ log_indstandard + open_water_day + log_NASC_zoo
##
## Df Sum of Sq RSS AIC
## + surf_temp_degC 1 0.42523 31.217 -798.53
## + surf_sal_kgm3 1 0.19908 31.443 -796.08
## <none> 31.642 -795.95
## - log_NASC_zoo 1 1.15898 32.801 -785.75
## - log_indstandard 1 1.60505 33.247 -781.17
## - open_water_day 1 1.72326 33.365 -779.97
##
## Step: AIC=-798.53
## fish_cond ~ log_indstandard + open_water_day + log_NASC_zoo +
## surf_temp_degC
##
## Df Sum of Sq RSS AIC
## <none> 31.217 -798.53
## + surf_sal_kgm3 1 0.05957 31.157 -797.18
## - surf_temp_degC 1 0.42523 31.642 -795.95
## - log_indstandard 1 0.73589 31.953 -792.63
## - log_NASC_zoo 1 1.54853 32.765 -784.12
## - open_water_day 1 1.65640 32.873 -783.00## Step Df Deviance Resid. Df Resid. Dev AIC
## 1 NA NA 338 35.06503 -767.1218
## 2 + log_indstandard -1 1.6221189 337 33.44291 -781.1784
## 3 + open_water_day -1 0.6420759 336 32.80083 -785.7502
## 4 + log_NASC_zoo -1 1.1589850 335 31.64185 -795.9452
## 5 + surf_temp_degC -1 0.4252313 334 31.21661 -798.5318##
## Call:
## lm(formula = fish_cond ~ log_indstandard + open_water_day + log_NASC_zoo +
## surf_temp_degC, data = dfish)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.24848 -0.18169 -0.00337 0.19715 1.26397
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.2207412 0.0435009 -5.074 6.46e-07 ***
## log_indstandard -0.0682597 0.0243264 -2.806 0.00531 **
## open_water_day 0.0027234 0.0006469 4.210 3.29e-05 ***
## log_NASC_zoo -0.1582352 0.0388743 -4.070 5.86e-05 ***
## surf_temp_degC 0.0195189 0.0091509 2.133 0.03365 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3057 on 334 degrees of freedom
## Multiple R-squared: 0.1098, Adjusted R-squared: 0.09909
## F-statistic: 10.29 on 4 and 334 DF, p-value: 7.155e-08## log_indstandard open_water_day log_NASC_zoo surf_temp_degC
## 1.242500 1.786072 2.096606 1.633757
Les conditions environnementales expliquent mal la variabilité du succès d’alimentation (\(R^2\) = 0.099089), même si presque toutes les variables incluses dans le modèle de départ restent significatives, sauf la salinité.
On va maintenant vérifier avec des modèles mixtes l’influence possible de l’hétérogénéité régionale.
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.855867 (tol = 0.002, component 1)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: fish_cond ~ log_indstandard + open_water_day + surf_temp_degC +
## log_NASC_zoo + (log_indstandard + open_water_day + surf_temp_degC +
## log_NASC_zoo | region)
## Data: dfish.LMER
##
## REML criterion at convergence: 127.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.2679 -0.5721 -0.0506 0.6165 3.6754
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## region (Intercept) 9.873e-02 0.314208
## log_indstandard 5.523e-02 0.235008 0.51
## open_water_day 2.331e-05 0.004829 -0.43 0.55
## surf_temp_degC 2.573e-03 0.050725 0.90 0.09 -0.78
## log_NASC_zoo 3.989e-02 0.199732 -0.49 0.48 0.97 -0.81
## Residual 7.187e-02 0.268093
## Number of obs: 314, groups: region, 7
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -0.171375 0.140749 4.567924 -1.218 0.2825
## log_indstandard 0.002826 0.097827 5.034503 0.029 0.9781
## open_water_day 0.006397 0.002224 4.541592 2.876 0.0389 *
## surf_temp_degC 0.016453 0.021925 5.833998 0.750 0.4822
## log_NASC_zoo -0.284838 0.104548 4.194887 -2.724 0.0501 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) lg_nds opn_w_ srf__C
## lg_ndstndrd 0.500
## open_wtr_dy -0.356 0.495
## srf_tmp_dgC 0.605 0.098 -0.554
## log_NASC_zo -0.364 0.314 0.372 -0.613
## convergence code: 0
## Model failed to converge with max|grad| = 0.855867 (tol = 0.002, component 1)## # Intraclass Correlation Coefficient
##
## Adjusted ICC: 0.599
## Conditional ICC: 0.543## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 1.46162 (tol = 0.002, component 1)## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: large eigenvalue ratio
## - Rescale variables?## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.0241952 (tol = 0.002, component 1)## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## unable to evaluate scaled gradient## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge: degenerate Hessian with 1 negative eigenvalues## Warning: Model failed to converge with 1 negative eigenvalue: -3.4e+00## boundary (singular) fit: see ?isSingular## ANOVA-like table for random-effects: Single term deletions
##
## Model:
## fish_cond ~ log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo + (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region)
## npar
## <none> 21
## log_indstandard in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 16
## open_water_day in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 16
## surf_temp_degC in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 16
## log_NASC_zoo in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 16
## logLik
## <none> -63.532
## log_indstandard in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) -73.430
## open_water_day in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) -66.691
## surf_temp_degC in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) -75.982
## log_NASC_zoo in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) -66.343
## AIC
## <none> 169.06
## log_indstandard in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 178.86
## open_water_day in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 165.38
## surf_temp_degC in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 183.97
## log_NASC_zoo in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 164.69
## LRT
## <none>
## log_indstandard in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 19.7952
## open_water_day in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 6.3169
## surf_temp_degC in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 24.9004
## log_NASC_zoo in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 5.6207
## Df
## <none>
## log_indstandard in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 5
## open_water_day in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 5
## surf_temp_degC in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 5
## log_NASC_zoo in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 5
## Pr(>Chisq)
## <none>
## log_indstandard in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 0.0013652
## open_water_day in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 0.2765949
## surf_temp_degC in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 0.0001456
## log_NASC_zoo in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 0.3448946
##
## <none>
## log_indstandard in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) **
## open_water_day in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region)
## surf_temp_degC in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) ***
## log_NASC_zoo in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## boundary (singular) fit: see ?isSingular## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: fish_cond ~ log_indstandard + surf_temp_degC + open_water_day +
## log_NASC_zoo + (log_indstandard + surf_temp_degC | region)
## Data: dfish.LMER
##
## REML criterion at convergence: 139.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.0273 -0.5893 -0.0353 0.6251 3.5492
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## region (Intercept) 0.099818 0.31594
## log_indstandard 0.049961 0.22352 0.96
## surf_temp_degC 0.001201 0.03465 0.36 0.62
## Residual 0.077834 0.27899
## Number of obs: 314, groups: region, 7
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -0.201608 0.135153 3.249577 -1.492 0.226
## log_indstandard -0.013854 0.092361 4.219092 -0.150 0.888
## surf_temp_degC 0.031299 0.017203 5.259098 1.819 0.126
## open_water_day 0.004748 0.001049 38.798373 4.528 5.54e-05 ***
## log_NASC_zoo -0.291883 0.059262 101.387802 -4.925 3.28e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) lg_nds srf__C opn_w_
## lg_ndstndrd 0.903
## srf_tmp_dgC 0.223 0.526
## open_wtr_dy -0.084 0.105 0.022
## log_NASC_zo -0.051 -0.153 -0.226 -0.755
## convergence code: 0
## boundary (singular) fit: see ?isSingular## # Intraclass Correlation Coefficient
##
## Adjusted ICC: 0.234
## Conditional ICC: 0.204## [[1]]## `geom_smooth()` using formula 'y ~ x'
##
## [[2]]
## [[2]]$region## `geom_smooth()` using formula 'y ~ x'
##
##
## [[3]]
##
## [[4]]## `geom_smooth()` using formula 'y ~ x'
SANS MS 2010: Modèles de succès alimentaire
Succès alimentaire et environnement
Modèles de régression linéaire
On va établir les modèles de régression linéaire multiples pour essayer d’expliquer la variabilité du succès alimentaire des poissons échantillonnés.
Lorsque pertinent, nous utiliserons des modèles à effet mixtes aléatoires pour tenir compte de la forte hétérogénéité spatiale de notre échantillonnage.
## Start: AIC=-533.74
## log_feeding_success ~ 1
##
## Df Sum of Sq RSS AIC
## + open_water_day 1 5.7894 64.012 -561.09
## + log_NASC_zoo 1 4.4340 65.368 -553.98
## + surf_sal_kgm3 1 2.7691 67.033 -545.46
## + log_indstandard 1 0.7288 69.073 -535.29
## <none> 69.802 -533.74
## + surf_temp_degC 1 0.1300 69.672 -532.37
##
## Step: AIC=-561.09
## log_feeding_success ~ open_water_day
##
## Df Sum of Sq RSS AIC
## + log_NASC_zoo 1 0.4661 63.546 -561.57
## + log_indstandard 1 0.4643 63.548 -561.56
## + surf_sal_kgm3 1 0.3906 63.622 -561.16
## <none> 64.012 -561.09
## + surf_temp_degC 1 0.2796 63.733 -560.57
## - open_water_day 1 5.7894 69.802 -533.74
##
## Step: AIC=-561.57
## log_feeding_success ~ open_water_day + log_NASC_zoo
##
## Df Sum of Sq RSS AIC
## + surf_temp_degC 1 0.70654 62.840 -563.36
## + log_indstandard 1 0.41805 63.128 -561.80
## <none> 63.546 -561.57
## + surf_sal_kgm3 1 0.34092 63.205 -561.39
## - log_NASC_zoo 1 0.46611 64.012 -561.09
## - open_water_day 1 1.82156 65.368 -553.98
##
## Step: AIC=-563.36
## log_feeding_success ~ open_water_day + log_NASC_zoo + surf_temp_degC
##
## Df Sum of Sq RSS AIC
## + log_indstandard 1 1.26168 61.578 -568.23
## <none> 62.840 -563.36
## + surf_sal_kgm3 1 0.05008 62.789 -561.63
## - surf_temp_degC 1 0.70654 63.546 -561.57
## - log_NASC_zoo 1 0.89305 63.733 -560.57
## - open_water_day 1 1.91649 64.756 -555.17
##
## Step: AIC=-568.23
## log_feeding_success ~ open_water_day + log_NASC_zoo + surf_temp_degC +
## log_indstandard
##
## Df Sum of Sq RSS AIC
## <none> 61.578 -568.23
## + surf_sal_kgm3 1 0.34054 61.237 -568.11
## - log_NASC_zoo 1 1.15837 62.736 -563.91
## - log_indstandard 1 1.26168 62.840 -563.36
## - surf_temp_degC 1 1.55017 63.128 -561.80
## - open_water_day 1 1.91256 63.490 -559.86## Step Df Deviance Resid. Df Resid. Dev AIC
## 1 NA NA 338 69.80162 -533.7363
## 2 + open_water_day -1 5.7894295 337 64.01219 -561.0881
## 3 + log_NASC_zoo -1 0.4661140 336 63.54607 -561.5656
## 4 + surf_temp_degC -1 0.7065431 335 62.83953 -563.3560
## 5 + log_indstandard -1 1.2616830 334 61.57785 -568.2316##
## Call:
## lm(formula = log_feeding_success ~ open_water_day + log_NASC_zoo +
## surf_temp_degC + log_indstandard, data = dfish)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.65508 -0.23667 0.05148 0.29186 1.06973
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.1732285 0.0610967 -51.938 < 2e-16 ***
## open_water_day 0.0029264 0.0009086 3.221 0.00140 **
## log_NASC_zoo 0.1368568 0.0545987 2.507 0.01266 *
## surf_temp_degC -0.0372677 0.0128523 -2.900 0.00398 **
## log_indstandard -0.0893786 0.0341663 -2.616 0.00930 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4294 on 334 degrees of freedom
## Multiple R-squared: 0.1178, Adjusted R-squared: 0.1073
## F-statistic: 11.15 on 4 and 334 DF, p-value: 1.674e-08## open_water_day log_NASC_zoo surf_temp_degC log_indstandard
## 1.786072 2.096606 1.633757 1.242500
Les conditions environnementales expliquent mal la variabilité du succès d’alimentation.
Seulement l’abondance de larves, l’abondance de macrozooplancton révélée par l’acoustique et le nombre de jours depuis la débâcle des poissons explique 16 % de la variance observée (\(R^2\) = 0.1072512)
On va maintenant vérifier avec des modèles mixtes l’influence possible de l’hétérogénéité régionale.
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 1.34791 (tol = 0.002, component 1)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula:
## log_feeding_success ~ log_indstandard + open_water_day + log_NASC_zoo +
## (log_indstandard + open_water_day + log_NASC_zoo | region)
## Data: dfish.LMER2
##
## REML criterion at convergence: 315.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3965 -0.4430 0.0316 0.6346 2.6870
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## region (Intercept) 1.750e-01 0.418315
## log_indstandard 6.363e-02 0.252241 1.00
## open_water_day 3.165e-05 0.005626 0.98 0.98
## log_NASC_zoo 2.145e-01 0.463148 -0.95 -0.95 -0.99
## Residual 1.485e-01 0.385394
## Number of obs: 298, groups: region, 7
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -3.189695 0.184501 3.989336 -17.288 6.7e-05 ***
## log_indstandard -0.120722 0.106226 4.656310 -1.136 0.311
## open_water_day -0.001764 0.002576 2.684021 -0.685 0.548
## log_NASC_zoo 0.376588 0.195547 3.115210 1.926 0.146
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) lg_nds opn_w_
## lg_ndstndrd 0.963
## open_wtr_dy 0.665 0.794
## log_NASC_zo -0.759 -0.821 -0.933
## convergence code: 0
## Model failed to converge with max|grad| = 1.34791 (tol = 0.002, component 1)## # Intraclass Correlation Coefficient
##
## Adjusted ICC: 0.248
## Conditional ICC: 0.212## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## unable to evaluate scaled gradient## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge: degenerate Hessian with 1 negative eigenvalues## Warning: Model failed to converge with 1 negative eigenvalue: -7.0e+00## boundary (singular) fit: see ?isSingular
## boundary (singular) fit: see ?isSingular## Warning: Model failed to converge with 1 negative eigenvalue: -1.1e+01## ANOVA-like table for random-effects: Single term deletions
##
## Model:
## log_feeding_success ~ log_indstandard + open_water_day + log_NASC_zoo + (log_indstandard + open_water_day + log_NASC_zoo | region)
## npar
## <none> 15
## log_indstandard in (log_indstandard + open_water_day + log_NASC_zoo | region) 11
## open_water_day in (log_indstandard + open_water_day + log_NASC_zoo | region) 11
## log_NASC_zoo in (log_indstandard + open_water_day + log_NASC_zoo | region) 11
## logLik
## <none> -157.63
## log_indstandard in (log_indstandard + open_water_day + log_NASC_zoo | region) -165.20
## open_water_day in (log_indstandard + open_water_day + log_NASC_zoo | region) -160.81
## log_NASC_zoo in (log_indstandard + open_water_day + log_NASC_zoo | region) -164.95
## AIC
## <none> 345.26
## log_indstandard in (log_indstandard + open_water_day + log_NASC_zoo | region) 352.39
## open_water_day in (log_indstandard + open_water_day + log_NASC_zoo | region) 343.62
## log_NASC_zoo in (log_indstandard + open_water_day + log_NASC_zoo | region) 351.91
## LRT
## <none>
## log_indstandard in (log_indstandard + open_water_day + log_NASC_zoo | region) 15.1292
## open_water_day in (log_indstandard + open_water_day + log_NASC_zoo | region) 6.3605
## log_NASC_zoo in (log_indstandard + open_water_day + log_NASC_zoo | region) 14.6454
## Df
## <none>
## log_indstandard in (log_indstandard + open_water_day + log_NASC_zoo | region) 4
## open_water_day in (log_indstandard + open_water_day + log_NASC_zoo | region) 4
## log_NASC_zoo in (log_indstandard + open_water_day + log_NASC_zoo | region) 4
## Pr(>Chisq)
## <none>
## log_indstandard in (log_indstandard + open_water_day + log_NASC_zoo | region) 0.004441
## open_water_day in (log_indstandard + open_water_day + log_NASC_zoo | region) 0.173796
## log_NASC_zoo in (log_indstandard + open_water_day + log_NASC_zoo | region) 0.005496
##
## <none>
## log_indstandard in (log_indstandard + open_water_day + log_NASC_zoo | region) **
## open_water_day in (log_indstandard + open_water_day + log_NASC_zoo | region)
## log_NASC_zoo in (log_indstandard + open_water_day + log_NASC_zoo | region) **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## boundary (singular) fit: see ?isSingular## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula:
## log_feeding_success ~ open_water_day + log_NASC_zoo + log_indstandard +
## (log_NASC_zoo + log_indstandard | region)
## Data: dfish.LMER2
##
## REML criterion at convergence: 321.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.9021 -0.4346 0.0528 0.6270 2.7119
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## region (Intercept) 0.15756 0.3969
## log_NASC_zoo 0.04746 0.2179 -1.00
## log_indstandard 0.03834 0.1958 1.00 -1.00
## Residual 0.15401 0.3924
## Number of obs: 298, groups: region, 7
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -3.2977965 0.1774771 4.2194966 -18.582 3.3e-05 ***
## open_water_day 0.0002516 0.0013291 35.3121551 0.189 0.8510
## log_NASC_zoo 0.3132350 0.1130129 9.1161960 2.772 0.0214 *
## log_indstandard -0.1641757 0.0865540 4.1175135 -1.897 0.1287
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) opn_w_ l_NASC
## open_wtr_dy -0.148
## log_NASC_zo -0.682 -0.521
## lg_ndstndrd 0.956 0.037 -0.724
## convergence code: 0
## boundary (singular) fit: see ?isSingular## Warning: Can't compute random effect variances. Some variance components equal zero. Your model may suffer from singulariy.
## Solution: Respecify random structure!
## You may also decrease the 'tolerance' level to enforce the calculation of random effect variances.## [1] NA## [[1]]## `geom_smooth()` using formula 'y ~ x'
##
## [[2]]
## [[2]]$region## `geom_smooth()` using formula 'y ~ x'
##
##
## [[3]]
##
## [[4]]## `geom_smooth()` using formula 'y ~ x'
Ajouter les régions comme effet aléatoire est plus rigoureux d’un point de vue de l’analyse de nos résultats, et cela permet de tenir compte de la variabilité de l’effet des variables explicatives sur le succès alimentaire selon les régions, en particulier de la densité de zooplancton observée par l’acoustique et la densité de larves.
Condition et environnement
Modèles de régression linéaire
On va établir les modèles de régression linéaire multiples pour essayer d’expliquer la variabilité de l’indice de condition des poissons échantillonnés.
Lorsque pertinent, nous utiliserons des modèles à effet mixtes aléatoires pour tenir compte de la forte hétérogénéité spatiale de notre échantillonnage.
## Start: AIC=-739.58
## fish_cond ~ 1
##
## Df Sum of Sq RSS AIC
## + surf_temp_degC 1 2.07875 30.438 -758.92
## + log_indstandard 1 1.87123 30.645 -756.72
## + open_water_day 1 0.96473 31.552 -747.31
## + surf_sal_kgm3 1 0.27061 32.246 -740.28
## <none> 32.516 -739.58
## + log_NASC_zoo 1 0.00059 32.516 -737.59
##
## Step: AIC=-758.92
## fish_cond ~ surf_temp_degC
##
## Df Sum of Sq RSS AIC
## + log_indstandard 1 0.68386 29.754 -764.26
## + log_NASC_zoo 1 0.30745 30.130 -760.20
## + open_water_day 1 0.28399 30.154 -759.95
## <none> 30.438 -758.92
## + surf_sal_kgm3 1 0.10200 30.336 -758.00
## - surf_temp_degC 1 2.07875 32.516 -739.58
##
## Step: AIC=-764.26
## fish_cond ~ surf_temp_degC + log_indstandard
##
## Df Sum of Sq RSS AIC
## + open_water_day 1 0.38578 29.368 -766.47
## + log_NASC_zoo 1 0.19846 29.555 -764.42
## <none> 29.754 -764.26
## + surf_sal_kgm3 1 0.00357 29.750 -762.30
## - log_indstandard 1 0.68386 30.438 -758.92
## - surf_temp_degC 1 0.89138 30.645 -756.72
##
## Step: AIC=-766.47
## fish_cond ~ surf_temp_degC + log_indstandard + open_water_day
##
## Df Sum of Sq RSS AIC
## + log_NASC_zoo 1 1.08337 28.285 -776.61
## + surf_sal_kgm3 1 0.24991 29.118 -767.23
## <none> 29.368 -766.47
## - open_water_day 1 0.38578 29.754 -764.26
## - surf_temp_degC 1 0.45474 29.823 -763.51
## - log_indstandard 1 0.78565 30.154 -759.95
##
## Step: AIC=-776.61
## fish_cond ~ surf_temp_degC + log_indstandard + open_water_day +
## log_NASC_zoo
##
## Df Sum of Sq RSS AIC
## <none> 28.285 -776.61
## + surf_sal_kgm3 1 0.07463 28.210 -775.47
## - log_indstandard 1 0.61567 28.900 -771.66
## - surf_temp_degC 1 0.81030 29.095 -769.49
## - log_NASC_zoo 1 1.08337 29.368 -766.47
## - open_water_day 1 1.27070 29.555 -764.42## Step Df Deviance Resid. Df Resid. Dev AIC
## 1 NA NA 322 32.51626 -739.5796
## 2 + surf_temp_degC -1 2.0787485 321 30.43751 -758.9184
## 3 + log_indstandard -1 0.6838575 320 29.75365 -764.2582
## 4 + open_water_day -1 0.3857850 319 29.36787 -766.4736
## 5 + log_NASC_zoo -1 1.0833706 318 28.28450 -776.6143##
## Call:
## lm(formula = fish_cond ~ surf_temp_degC + log_indstandard + open_water_day +
## log_NASC_zoo, data = dfish_noMS2010)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.28151 -0.18214 -0.00804 0.19185 1.27752
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.2322484 0.0426260 -5.449 1.02e-07 ***
## surf_temp_degC 0.0307096 0.0101744 3.018 0.002747 **
## log_indstandard -0.0633111 0.0240640 -2.631 0.008929 **
## open_water_day 0.0024288 0.0006426 3.780 0.000187 ***
## log_NASC_zoo -0.1355068 0.0388270 -3.490 0.000551 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2982 on 318 degrees of freedom
## Multiple R-squared: 0.1301, Adjusted R-squared: 0.1192
## F-statistic: 11.89 on 4 and 318 DF, p-value: 5.111e-09## surf_temp_degC log_indstandard open_water_day log_NASC_zoo
## 1.473186 1.252682 1.810886 1.887320
Les conditions environnementales expliquent mal la variabilité du succès d’alimentation (\(R^2\) = 0.099089), même si presque toutes les variables incluses dans le modèle de départ restent significatives, sauf la salinité.
On va maintenant vérifier avec des modèles mixtes l’influence possible de l’hétérogénéité régionale.
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## unable to evaluate scaled gradient## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge: degenerate Hessian with 1 negative eigenvalues## Warning: Model failed to converge with 1 negative eigenvalue: -3.0e+01## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: fish_cond ~ log_indstandard + open_water_day + surf_temp_degC +
## log_NASC_zoo + (log_indstandard + open_water_day + surf_temp_degC +
## log_NASC_zoo | region)
## Data: dfish.LMER2
##
## REML criterion at convergence: 102.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3341 -0.5919 -0.0250 0.6003 3.7787
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## region (Intercept) 1.087e-01 0.329685
## log_indstandard 6.141e-02 0.247807 0.54
## open_water_day 3.112e-05 0.005578 -0.43 0.52
## surf_temp_degC 3.043e-03 0.055166 0.80 -0.06 -0.88
## log_NASC_zoo 3.384e-02 0.183965 -0.26 0.67 0.98 -0.78
## Residual 6.674e-02 0.258347
## Number of obs: 298, groups: region, 7
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -0.191111 0.145338 4.249693 -1.315 0.2550
## log_indstandard 0.001978 0.101632 5.121986 0.019 0.9852
## open_water_day 0.006821 0.002463 5.003354 2.769 0.0394 *
## surf_temp_degC 0.014272 0.023584 6.171566 0.605 0.5666
## log_NASC_zoo -0.281336 0.098526 3.331758 -2.855 0.0573 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) lg_nds opn_w_ srf__C
## lg_ndstndrd 0.529
## open_wtr_dy -0.361 0.485
## srf_tmp_dgC 0.530 -0.045 -0.679
## log_NASC_zo -0.212 0.428 0.395 -0.554
## convergence code: 0
## unable to evaluate scaled gradient
## Model failed to converge: degenerate Hessian with 1 negative eigenvalues## # Intraclass Correlation Coefficient
##
## Adjusted ICC: 0.649
## Conditional ICC: 0.582## boundary (singular) fit: see ?isSingular## Warning: Model failed to converge with 1 negative eigenvalue: -7.8e+00## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.0306855 (tol = 0.002, component 1)## boundary (singular) fit: see ?isSingular## Warning: Model failed to converge with 2 negative eigenvalues: -9.9e-01 -2.6e+00## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.677612 (tol = 0.002, component 1)## ANOVA-like table for random-effects: Single term deletions
##
## Model:
## fish_cond ~ log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo + (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region)
## npar
## <none> 21
## log_indstandard in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 16
## open_water_day in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 16
## surf_temp_degC in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 16
## log_NASC_zoo in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 16
## logLik
## <none> -51.458
## log_indstandard in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) -62.037
## open_water_day in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) -54.453
## surf_temp_degC in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) -62.966
## log_NASC_zoo in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) -52.561
## AIC
## <none> 144.92
## log_indstandard in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 156.07
## open_water_day in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 140.91
## surf_temp_degC in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 157.93
## log_NASC_zoo in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 137.12
## LRT
## <none>
## log_indstandard in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 21.1583
## open_water_day in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 5.9899
## surf_temp_degC in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 23.0164
## log_NASC_zoo in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 2.2047
## Df
## <none>
## log_indstandard in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 5
## open_water_day in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 5
## surf_temp_degC in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 5
## log_NASC_zoo in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 5
## Pr(>Chisq)
## <none>
## log_indstandard in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 0.0007561
## open_water_day in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 0.3072039
## surf_temp_degC in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 0.0003351
## log_NASC_zoo in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) 0.8201524
##
## <none>
## log_indstandard in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) ***
## open_water_day in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region)
## surf_temp_degC in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region) ***
## log_NASC_zoo in (log_indstandard + open_water_day + surf_temp_degC + log_NASC_zoo | region)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## boundary (singular) fit: see ?isSingular## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: fish_cond ~ log_indstandard + surf_temp_degC + open_water_day +
## log_NASC_zoo + (log_indstandard + surf_temp_degC | region)
## Data: dfish.LMER2
##
## REML criterion at convergence: 114.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.6387 -0.6106 -0.0384 0.6088 3.6413
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## region (Intercept) 0.202744 0.45027
## log_indstandard 0.061188 0.24736 0.91
## surf_temp_degC 0.003197 0.05654 -0.30 0.13
## Residual 0.071170 0.26678
## Number of obs: 298, groups: region, 7
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -0.132234 0.183808 3.918212 -0.719 0.512
## log_indstandard 0.004536 0.100617 4.274685 0.045 0.966
## surf_temp_degC 0.024655 0.024647 6.039159 1.000 0.356
## open_water_day 0.005464 0.001130 61.326611 4.836 9.27e-06 ***
## log_NASC_zoo -0.365325 0.063858 127.580770 -5.721 7.16e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) lg_nds srf__C opn_w_
## lg_ndstndrd 0.880
## srf_tmp_dgC -0.292 0.126
## open_wtr_dy -0.030 0.120 -0.028
## log_NASC_zo -0.066 -0.151 -0.106 -0.768
## convergence code: 0
## boundary (singular) fit: see ?isSingular## Warning: Can't compute random effect variances. Some variance components equal zero. Your model may suffer from singulariy.
## Solution: Respecify random structure!
## You may also decrease the 'tolerance' level to enforce the calculation of random effect variances.## [1] NA## [[1]]## `geom_smooth()` using formula 'y ~ x'
##
## [[2]]
## [[2]]$region## `geom_smooth()` using formula 'y ~ x'
##
##
## [[3]]
##
## [[4]]## `geom_smooth()` using formula 'y ~ x'
Section 3. Proies et succès alimentaire
Succès alimentaire et taille des proies
On explore les relations possibles entre le succès alimentaire et la taille des proies des poissons.
## log_feeding_success log_prey_max_um log_prey_min_um
## log_feeding_success 1.00 -0.14 -0.04
## log_prey_max_um -0.14 1.00 0.16
## log_prey_min_um -0.04 0.16 1.00
## log_prey_median_um -0.18 0.58 0.48
## log_prey_range_um -0.14 0.99 0.06
## log_total_preys 0.53 -0.17 -0.01
## log_prey_median_um log_prey_range_um log_total_preys
## log_feeding_success -0.18 -0.14 0.53
## log_prey_max_um 0.58 0.99 -0.17
## log_prey_min_um 0.48 0.06 -0.01
## log_prey_median_um 1.00 0.54 -0.16
## log_prey_range_um 0.54 1.00 -0.17
## log_total_preys -0.16 -0.17 1.00
##
## n= 339
##
##
## P
## log_feeding_success log_prey_max_um log_prey_min_um
## log_feeding_success 0.0075 0.4818
## log_prey_max_um 0.0075 0.0030
## log_prey_min_um 0.4818 0.0030
## log_prey_median_um 0.0007 0.0000 0.0000
## log_prey_range_um 0.0077 0.0000 0.3091
## log_total_preys 0.0000 0.0019 0.9255
## log_prey_median_um log_prey_range_um log_total_preys
## log_feeding_success 0.0007 0.0077 0.0000
## log_prey_max_um 0.0000 0.0000 0.0019
## log_prey_min_um 0.0000 0.3091 0.9255
## log_prey_median_um 0.0000 0.0030
## log_prey_range_um 0.0000 0.0016
## log_total_preys 0.0030 0.0016
Modèles de régression linéaire
On va établir les modèles de régression linéaire multiples pour essayer d’expliquer la variabilité du succes d’alimentation des poissons échantillonnés selon les propriétés de leur alimentation.
## Start: AIC=-533.74
## log_feeding_success ~ 1
##
## Df Sum of Sq RSS AIC
## + log_total_preys 1 19.9687 49.833 -645.97
## + log_prey_median_um 1 2.3678 67.434 -543.44
## + log_prey_max_um 1 1.4671 68.335 -538.94
## <none> 69.802 -533.74
##
## Step: AIC=-645.97
## log_feeding_success ~ log_total_preys
##
## Df Sum of Sq RSS AIC
## + log_prey_median_um 1 0.6899 49.143 -648.70
## <none> 49.833 -645.97
## + log_prey_max_um 1 0.2174 49.616 -645.46
## - log_total_preys 1 19.9687 69.802 -533.74
##
## Step: AIC=-648.7
## log_feeding_success ~ log_total_preys + log_prey_median_um
##
## Df Sum of Sq RSS AIC
## <none> 49.143 -648.70
## + log_prey_max_um 1 0.0001 49.143 -646.70
## - log_prey_median_um 1 0.6899 49.833 -645.97
## - log_total_preys 1 18.2907 67.434 -543.44## Step Df Deviance Resid. Df Resid. Dev AIC
## 1 NA NA 338 69.80162 -533.7363
## 2 + log_total_preys -1 19.9686885 337 49.83293 -645.9729
## 3 + log_prey_median_um -1 0.6898605 336 49.14307 -648.6986##
## Call:
## lm(formula = log_feeding_success ~ log_total_preys + log_prey_median_um,
## data = dfish)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.06386 -0.26001 0.01571 0.23974 1.34929
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.19187 0.25609 -12.464 <2e-16 ***
## log_total_preys 0.48518 0.04339 11.183 <2e-16 ***
## log_prey_median_um -0.20603 0.09487 -2.172 0.0306 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3824 on 336 degrees of freedom
## Multiple R-squared: 0.296, Adjusted R-squared: 0.2918
## F-statistic: 70.62 on 2 and 336 DF, p-value: < 2.2e-16## log_total_preys log_prey_median_um
## 1.026578 1.026578
Les caractéristiques de taille et d’abondance des proies expliquent assez bien la variabilité du succès d’alimentation (\(R^2\) = 0.2917702).
On va maintenant vérifier avec des modèles mixtes l’influence possible de l’hétérogénéité régionale.
## boundary (singular) fit: see ?isSingular## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: log_feeding_success ~ log_prey_median_um + log_total_preys +
## (log_prey_median_um + log_total_preys | region)
## Data: dfish
##
## REML criterion at convergence: 254.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.8097 -0.6250 0.0844 0.5691 3.4137
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## region (Intercept) 0.35656 0.5971
## log_prey_median_um 0.04393 0.2096 -0.62
## log_total_preys 0.09644 0.3106 -0.74 -0.07
## Residual 0.11045 0.3323
## Number of obs: 339, groups: region, 9
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -3.1138 0.3081 12.1699 -10.108 2.83e-07 ***
## log_prey_median_um -0.2221 0.1134 10.8817 -1.959 0.07628 .
## log_total_preys 0.4830 0.1138 7.9575 4.245 0.00285 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) lg_p__
## lg_pry_mdn_ -0.810
## lg_ttl_prys -0.549 -0.030
## convergence code: 0
## boundary (singular) fit: see ?isSingular## Warning: Can't compute random effect variances. Some variance components equal zero. Your model may suffer from singulariy.
## Solution: Respecify random structure!
## You may also decrease the 'tolerance' level to enforce the calculation of random effect variances.## [1] NA## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.00271089 (tol = 0.002, component 1)## boundary (singular) fit: see ?isSingular## ANOVA-like table for random-effects: Single term deletions
##
## Model:
## log_feeding_success ~ log_prey_median_um + log_total_preys + (log_prey_median_um + log_total_preys | region)
## npar
## <none> 10
## log_prey_median_um in (log_prey_median_um + log_total_preys | region) 7
## log_total_preys in (log_prey_median_um + log_total_preys | region) 7
## logLik
## <none> -127.46
## log_prey_median_um in (log_prey_median_um + log_total_preys | region) -130.24
## log_total_preys in (log_prey_median_um + log_total_preys | region) -142.27
## AIC
## <none> 274.92
## log_prey_median_um in (log_prey_median_um + log_total_preys | region) 274.49
## log_total_preys in (log_prey_median_um + log_total_preys | region) 298.54
## LRT
## <none>
## log_prey_median_um in (log_prey_median_um + log_total_preys | region) 5.5662
## log_total_preys in (log_prey_median_um + log_total_preys | region) 29.6229
## Df
## <none>
## log_prey_median_um in (log_prey_median_um + log_total_preys | region) 3
## log_total_preys in (log_prey_median_um + log_total_preys | region) 3
## Pr(>Chisq)
## <none>
## log_prey_median_um in (log_prey_median_um + log_total_preys | region) 0.1347
## log_total_preys in (log_prey_median_um + log_total_preys | region) 1.657e-06
##
## <none>
## log_prey_median_um in (log_prey_median_um + log_total_preys | region)
## log_total_preys in (log_prey_median_um + log_total_preys | region) ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.00271089 (tol = 0.002, component 1)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: log_feeding_success ~ log_prey_median_um + log_total_preys +
## (log_total_preys | region)
## Data: dfish
##
## REML criterion at convergence: 260.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.7559 -0.6281 0.0659 0.5840 3.3444
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## region (Intercept) 0.25094 0.5009
## log_total_preys 0.09799 0.3130 -0.97
## Residual 0.11266 0.3357
## Number of obs: 339, groups: region, 9
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -3.03188 0.29555 45.60898 -10.258 1.99e-13 ***
## log_prey_median_um -0.25889 0.08752 330.97881 -2.958 0.00332 **
## log_total_preys 0.49163 0.11521 8.14244 4.267 0.00263 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) lg_p__
## lg_pry_mdn_ -0.773
## lg_ttl_prys -0.657 0.056
## convergence code: 0
## Model failed to converge with max|grad| = 0.00271089 (tol = 0.002, component 1)## # Intraclass Correlation Coefficient
##
## Adjusted ICC: 0.248
## Conditional ICC: 0.173## [[1]]## `geom_smooth()` using formula 'y ~ x'
##
## [[2]]
## [[2]]$region## `geom_smooth()` using formula 'y ~ x'
##
##
## [[3]]
##
## [[4]]## `geom_smooth()` using formula 'y ~ x'
Ajouter les régions comme effet aléatoire permet de tenir compte de la variabilité de l’abondance totale de proies sur le succès alimentaire selon les régions.
Succès alimentaire et composition des proies
On vérifie la relation entre le «feeding success» et la composition des proies.
PASCALE : pourquoi des matrices de présence/absence ?
## Start: AIC=-533.74
## log_feeding_success ~ 1
##
## Df Sum of Sq RSS AIC
## + log_calanus.sp.n 1 13.2476 56.554 -603.08
## + log_pseudocalanus.sp.c 1 11.6448 58.157 -593.61
## + log_other.calanus.sp.c 1 11.0177 58.784 -589.97
## + log_calanus.glacialis.c 1 9.8083 59.993 -583.07
## + log_other.calanoid.sp.c 1 5.9967 63.805 -562.19
## + log_pseudocalanus.sp.n 1 4.4494 65.352 -554.06
## + log_egg 1 1.7610 68.041 -540.40
## + log_appendicularia 1 0.5802 69.221 -534.57
## + log_cyclopoidae.sp.c 1 0.5310 69.271 -534.32
## <none> 69.802 -533.74
## + log_other 1 0.3114 69.490 -533.25
## + log_other.copepodite.and.n 1 0.0494 69.752 -531.98
##
## Step: AIC=-603.08
## log_feeding_success ~ log_calanus.sp.n
##
## Df Sum of Sq RSS AIC
## + log_other.calanus.sp.c 1 10.3309 46.223 -669.46
## + log_calanus.glacialis.c 1 8.2003 48.354 -654.19
## + log_pseudocalanus.sp.c 1 4.3782 52.176 -628.40
## + log_other.calanoid.sp.c 1 2.9028 53.651 -618.95
## + log_other.copepodite.and.n 1 1.0663 55.488 -607.54
## + log_cyclopoidae.sp.c 1 0.5545 55.999 -604.42
## + log_pseudocalanus.sp.n 1 0.5294 56.025 -604.27
## + log_egg 1 0.4900 56.064 -604.03
## <none> 56.554 -603.08
## + log_other 1 0.1243 56.430 -601.83
## + log_appendicularia 1 0.0267 56.527 -601.24
## - log_calanus.sp.n 1 13.2476 69.802 -533.74
##
## Step: AIC=-669.46
## log_feeding_success ~ log_calanus.sp.n + log_other.calanus.sp.c
##
## Df Sum of Sq RSS AIC
## + log_calanus.glacialis.c 1 1.7248 44.498 -680.36
## + log_cyclopoidae.sp.c 1 1.6516 44.571 -679.80
## + log_pseudocalanus.sp.c 1 1.3816 44.842 -677.75
## + log_other.copepodite.and.n 1 1.3420 44.881 -677.45
## + log_egg 1 0.7877 45.435 -673.29
## + log_other.calanoid.sp.c 1 0.6886 45.534 -672.55
## <none> 46.223 -669.46
## + log_appendicularia 1 0.0254 46.198 -667.65
## + log_pseudocalanus.sp.n 1 0.0124 46.211 -667.56
## + log_other 1 0.0068 46.216 -667.51
## - log_other.calanus.sp.c 1 10.3309 56.554 -603.08
## - log_calanus.sp.n 1 12.5608 58.784 -589.97
##
## Step: AIC=-680.36
## log_feeding_success ~ log_calanus.sp.n + log_other.calanus.sp.c +
## log_calanus.glacialis.c
##
## Df Sum of Sq RSS AIC
## + log_cyclopoidae.sp.c 1 2.0476 42.451 -694.33
## + log_other.copepodite.and.n 1 1.2758 43.222 -688.22
## + log_egg 1 0.6501 43.848 -683.35
## + log_pseudocalanus.sp.c 1 0.5441 43.954 -682.53
## + log_other.calanoid.sp.c 1 0.3675 44.131 -681.17
## <none> 44.498 -680.36
## + log_other 1 0.1577 44.341 -679.56
## + log_appendicularia 1 0.0006 44.498 -678.36
## + log_pseudocalanus.sp.n 1 0.0002 44.498 -678.36
## - log_calanus.glacialis.c 1 1.7248 46.223 -669.46
## - log_other.calanus.sp.c 1 3.8554 48.354 -654.19
## - log_calanus.sp.n 1 11.8392 56.337 -602.38
##
## Step: AIC=-694.33
## log_feeding_success ~ log_calanus.sp.n + log_other.calanus.sp.c +
## log_calanus.glacialis.c + log_cyclopoidae.sp.c
##
## Df Sum of Sq RSS AIC
## + log_egg 1 1.5050 40.946 -704.56
## + log_pseudocalanus.sp.c 1 1.3338 41.117 -703.15
## + log_other.copepodite.and.n 1 0.6690 41.782 -697.71
## + log_other.calanoid.sp.c 1 0.5845 41.866 -697.03
## <none> 42.451 -694.33
## + log_appendicularia 1 0.0652 42.385 -692.85
## + log_other 1 0.0393 42.411 -692.64
## + log_pseudocalanus.sp.n 1 0.0005 42.450 -692.33
## - log_cyclopoidae.sp.c 1 2.0476 44.498 -680.36
## - log_calanus.glacialis.c 1 2.1208 44.571 -679.80
## - log_other.calanus.sp.c 1 4.2939 46.745 -663.66
## - log_calanus.sp.n 1 13.8868 56.337 -600.38
##
## Step: AIC=-704.56
## log_feeding_success ~ log_calanus.sp.n + log_other.calanus.sp.c +
## log_calanus.glacialis.c + log_cyclopoidae.sp.c + log_egg
##
## Df Sum of Sq RSS AIC
## + log_pseudocalanus.sp.c 1 0.8644 40.081 -709.80
## + log_other.copepodite.and.n 1 0.5389 40.407 -707.05
## + log_other.calanoid.sp.c 1 0.4781 40.468 -706.54
## <none> 40.946 -704.56
## + log_other 1 0.0437 40.902 -702.92
## + log_appendicularia 1 0.0281 40.918 -702.80
## + log_pseudocalanus.sp.n 1 0.0065 40.939 -702.62
## - log_egg 1 1.5050 42.451 -694.33
## - log_calanus.glacialis.c 1 1.9898 42.935 -690.48
## - log_cyclopoidae.sp.c 1 2.9025 43.848 -683.35
## - log_other.calanus.sp.c 1 4.8045 45.750 -668.95
## - log_calanus.sp.n 1 13.2667 54.212 -611.42
##
## Step: AIC=-709.8
## log_feeding_success ~ log_calanus.sp.n + log_other.calanus.sp.c +
## log_calanus.glacialis.c + log_cyclopoidae.sp.c + log_egg +
## log_pseudocalanus.sp.c
##
## Df Sum of Sq RSS AIC
## + log_other.copepodite.and.n 1 0.5256 39.556 -712.27
## <none> 40.081 -709.80
## + log_other.calanoid.sp.c 1 0.1976 39.884 -709.47
## + log_other 1 0.0577 40.024 -708.28
## + log_appendicularia 1 0.0357 40.046 -708.10
## + log_pseudocalanus.sp.n 1 0.0163 40.065 -707.93
## - log_pseudocalanus.sp.c 1 0.8644 40.946 -704.56
## - log_calanus.glacialis.c 1 0.9593 41.041 -703.78
## - log_egg 1 1.0357 41.117 -703.15
## - log_cyclopoidae.sp.c 1 3.4636 43.545 -683.70
## - log_other.calanus.sp.c 1 4.5162 44.597 -675.60
## - log_calanus.sp.n 1 9.8824 49.964 -637.09
##
## Step: AIC=-712.27
## log_feeding_success ~ log_calanus.sp.n + log_other.calanus.sp.c +
## log_calanus.glacialis.c + log_cyclopoidae.sp.c + log_egg +
## log_pseudocalanus.sp.c + log_other.copepodite.and.n
##
## Df Sum of Sq RSS AIC
## <none> 39.556 -712.27
## + log_other.calanoid.sp.c 1 0.1720 39.384 -711.75
## + log_other 1 0.0938 39.462 -711.08
## + log_appendicularia 1 0.0547 39.501 -710.74
## + log_pseudocalanus.sp.n 1 0.0018 39.554 -710.29
## - log_other.copepodite.and.n 1 0.5256 40.081 -709.80
## - log_pseudocalanus.sp.c 1 0.8511 40.407 -707.05
## - log_calanus.glacialis.c 1 0.9036 40.459 -706.61
## - log_egg 1 0.9356 40.491 -706.35
## - log_cyclopoidae.sp.c 1 2.6657 42.221 -692.16
## - log_other.calanus.sp.c 1 4.5750 44.131 -677.17
## - log_calanus.sp.n 1 10.4079 49.964 -635.09##
## Call:
## lm(formula = log_feeding_success ~ log_calanus.sp.n + log_other.calanus.sp.c +
## log_calanus.glacialis.c + log_cyclopoidae.sp.c + log_egg +
## log_pseudocalanus.sp.c + log_other.copepodite.and.n, data = prey_matrix_comb2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.09539 -0.18493 0.01806 0.22121 1.62874
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.35764 0.04112 -81.657 < 2e-16 ***
## log_calanus.sp.n 0.37886 0.04060 9.332 < 2e-16 ***
## log_other.calanus.sp.c 0.39468 0.06379 6.187 1.81e-09 ***
## log_calanus.glacialis.c 0.17291 0.06288 2.750 0.00629 **
## log_cyclopoidae.sp.c -0.18905 0.04003 -4.723 3.44e-06 ***
## log_egg 0.09598 0.03430 2.798 0.00544 **
## log_pseudocalanus.sp.c 0.12464 0.04671 2.669 0.00799 **
## log_other.copepodite.and.n -0.10762 0.05132 -2.097 0.03674 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3457 on 331 degrees of freedom
## Multiple R-squared: 0.4333, Adjusted R-squared: 0.4213
## F-statistic: 36.16 on 7 and 331 DF, p-value: < 2.2e-16## log_calanus.sp.n log_other.calanus.sp.c
## 1.396197 1.467152
## log_calanus.glacialis.c log_cyclopoidae.sp.c
## 1.680559 1.459761
## log_egg log_pseudocalanus.sp.c
## 1.167905 1.728383
## log_other.copepodite.and.n
## 1.194378
Les caractéristiques taxonomiques des proies expliquent bien la variabilité du succès d’alimentation (\(R^2\) = 0.4213288).
On va maintenant vérifier avec des modèles mixtes l’influence possible de l’hétérogénéité régionale.
## boundary (singular) fit: see ?isSingular## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: log_feeding_success ~ log_calanus.glacialis.c + log_calanus.sp.n +
## log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c +
## log_other.copepodite.and.n + log_pseudocalanus.sp.c + (log_calanus.glacialis.c +
## log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c +
## log_other.copepodite.and.n + log_pseudocalanus.sp.c | region)
## Data: prey_matrix_comb2
##
## REML criterion at convergence: 169.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.9206 -0.5911 0.0777 0.5792 4.4637
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## region (Intercept) 0.078466 0.28012
## log_calanus.glacialis.c 0.040477 0.20119 -0.68
## log_calanus.sp.n 0.121611 0.34873 -0.98 0.75
## log_cyclopoidae.sp.c 0.023775 0.15419 0.02 0.56 0.00
## log_egg 0.010962 0.10470 -0.62 0.32 0.67 -0.61
## log_other.calanus.sp.c 0.023737 0.15407 0.83 -0.79 -0.90 -0.30
## log_other.copepodite.and.n 0.013645 0.11681 0.62 -0.34 -0.71 0.52
## log_pseudocalanus.sp.c 0.007571 0.08701 0.67 -0.75 -0.64 -0.68
## Residual 0.076533 0.27665
##
##
##
##
##
##
## -0.40
## -0.93 0.58
## 0.12 0.76 -0.04
##
## Number of obs: 339, groups: region, 9
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -3.42024 0.10159 7.82466 -33.666 9.48e-10 ***
## log_calanus.glacialis.c 0.25686 0.08943 5.13877 2.872 0.03382 *
## log_calanus.sp.n 0.34672 0.12251 7.73482 2.830 0.02292 *
## log_cyclopoidae.sp.c -0.15088 0.06521 8.31940 -2.314 0.04819 *
## log_egg 0.09855 0.04688 8.23703 2.102 0.06773 .
## log_other.calanus.sp.c 0.27229 0.07767 7.93291 3.506 0.00812 **
## log_other.copepodite.and.n 0.02250 0.05942 8.65831 0.379 0.71400
## log_pseudocalanus.sp.c 0.16701 0.05127 8.95189 3.257 0.00995 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) lg_clns.g. lg_clns.s. lg_cy.. log_gg lg_thr.cl.. lg_thr.cp..
## lg_clns.gl. -0.505
## lg_clns.sp. -0.920 0.541
## lg_cyclpd.. 0.020 0.336 -0.035
## log_egg -0.528 0.229 0.484 -0.466
## lg_thr.cl.. 0.459 -0.615 -0.541 -0.172 -0.151
## lg_thr.cp.. 0.311 -0.139 -0.512 0.217 -0.458 0.224
## lg_psdcln.. 0.365 -0.445 -0.420 -0.455 0.018 0.212 -0.011
## convergence code: 0
## boundary (singular) fit: see ?isSingular## Warning: Can't compute random effect variances. Some variance components equal zero. Your model may suffer from singulariy.
## Solution: Respecify random structure!
## You may also decrease the 'tolerance' level to enforce the calculation of random effect variances.## [1] NA## boundary (singular) fit: see ?isSingular## Warning: Model failed to converge with 1 negative eigenvalue: -1.7e-01## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.0503473 (tol = 0.002, component 1)## boundary (singular) fit: see ?isSingular
## boundary (singular) fit: see ?isSingular
## boundary (singular) fit: see ?isSingular
## boundary (singular) fit: see ?isSingular## Warning: Model failed to converge with 1 negative eigenvalue: -2.5e-02## boundary (singular) fit: see ?isSingular## ANOVA-like table for random-effects: Single term deletions
##
## Model:
## log_feeding_success ~ log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c + (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region)
## npar
## <none> 45
## log_calanus.glacialis.c in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 37
## log_calanus.sp.n in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 37
## log_cyclopoidae.sp.c in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 37
## log_egg in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 37
## log_other.calanus.sp.c in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 37
## log_other.copepodite.and.n in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 37
## log_pseudocalanus.sp.c in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 37
## logLik
## <none> -84.859
## log_calanus.glacialis.c in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) -88.155
## log_calanus.sp.n in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) -113.345
## log_cyclopoidae.sp.c in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) -90.173
## log_egg in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) -89.283
## log_other.calanus.sp.c in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) -87.012
## log_other.copepodite.and.n in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) -87.249
## log_pseudocalanus.sp.c in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) -86.348
## AIC
## <none> 259.72
## log_calanus.glacialis.c in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 250.31
## log_calanus.sp.n in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 300.69
## log_cyclopoidae.sp.c in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 254.35
## log_egg in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 252.56
## log_other.calanus.sp.c in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 248.03
## log_other.copepodite.and.n in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 248.50
## log_pseudocalanus.sp.c in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 246.70
## LRT
## <none>
## log_calanus.glacialis.c in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 6.592
## log_calanus.sp.n in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 56.973
## log_cyclopoidae.sp.c in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 10.629
## log_egg in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 8.847
## log_other.calanus.sp.c in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 4.307
## log_other.copepodite.and.n in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 4.780
## log_pseudocalanus.sp.c in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 2.978
## Df
## <none>
## log_calanus.glacialis.c in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 8
## log_calanus.sp.n in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 8
## log_cyclopoidae.sp.c in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 8
## log_egg in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 8
## log_other.calanus.sp.c in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 8
## log_other.copepodite.and.n in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 8
## log_pseudocalanus.sp.c in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 8
## Pr(>Chisq)
## <none>
## log_calanus.glacialis.c in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 0.5812
## log_calanus.sp.n in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 1.823e-09
## log_cyclopoidae.sp.c in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 0.2236
## log_egg in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 0.3554
## log_other.calanus.sp.c in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 0.8284
## log_other.copepodite.and.n in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 0.7808
## log_pseudocalanus.sp.c in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 0.9357
##
## <none>
## log_calanus.glacialis.c in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region)
## log_calanus.sp.n in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) ***
## log_cyclopoidae.sp.c in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region)
## log_egg in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region)
## log_other.calanus.sp.c in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region)
## log_other.copepodite.and.n in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region)
## log_pseudocalanus.sp.c in (log_calanus.glacialis.c + log_calanus.sp.n + log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: log_feeding_success ~ log_calanus.glacialis.c + log_calanus.sp.n +
## log_cyclopoidae.sp.c + log_egg + log_other.calanus.sp.c +
## log_pseudocalanus.sp.c + (log_calanus.sp.n | region)
## Data: prey_matrix_comb2
##
## REML criterion at convergence: 192.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.5824 -0.6211 0.0650 0.6073 4.5056
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## region (Intercept) 0.07105 0.2665
## log_calanus.sp.n 0.08018 0.2832 -0.89
## Residual 0.08652 0.2941
## Number of obs: 339, groups: region, 9
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -3.37438 0.09897 9.33169 -34.095 4.11e-11 ***
## log_calanus.glacialis.c 0.17874 0.05731 325.67994 3.119 0.001979 **
## log_calanus.sp.n 0.32551 0.10198 8.59927 3.192 0.011628 *
## log_cyclopoidae.sp.c -0.15587 0.04121 248.66547 -3.783 0.000195 ***
## log_egg 0.08859 0.03071 325.79180 2.885 0.004173 **
## log_other.calanus.sp.c 0.33073 0.05951 304.78073 5.557 5.98e-08 ***
## log_pseudocalanus.sp.c 0.16982 0.04436 320.38963 3.828 0.000155 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) lg_clns.g. lg_clns.s. lg_cy.. log_gg lg_...
## lg_clns.gl. -0.031
## lg_clns.sp. -0.836 0.012
## lg_cyclpd.. -0.031 0.017 -0.105
## log_egg -0.161 0.092 0.008 -0.219
## lg_thr.cl.. -0.101 -0.473 0.038 0.027 0.074
## lg_psdcln.. 0.012 -0.299 -0.101 -0.264 -0.137 -0.138## # Intraclass Correlation Coefficient
##
## Adjusted ICC: 0.311
## Conditional ICC: 0.186## [[1]]## `geom_smooth()` using formula 'y ~ x'
##
## [[2]]
## [[2]]$region## `geom_smooth()` using formula 'y ~ x'
##
##
## [[3]]
##
## [[4]]## `geom_smooth()` using formula 'y ~ x'
Ajouter les régions comme effet aléatoire permet de tenir compte de la variabilité de l’abondance des nauplii de Calanus sp parmi les proies sur le succès alimentaire selon les régions.
Condition et composition des proies
On vérifie la relation entre la condition et la composition des proies.
## Start: AIC=-767.12
## fish_cond ~ 1
##
## Df Sum of Sq RSS AIC
## + log_pseudocalanus.sp.c 1 1.99037 33.075 -784.93
## + log_egg 1 0.98912 34.076 -774.82
## + log_cyclopoidae.sp.c 1 0.56934 34.496 -770.67
## + log_calanus.sp.n 1 0.33504 34.730 -768.38
## + log_calanus.glacialis.c 1 0.24442 34.821 -767.49
## + log_other 1 0.21063 34.854 -767.16
## <none> 35.065 -767.12
## + log_other.copepodite.and.n 1 0.17217 34.893 -766.79
## + log_appendicularia 1 0.13874 34.926 -766.47
## + log_other.calanoid.sp.c 1 0.11272 34.952 -766.21
## + log_other.calanus.sp.c 1 0.09264 34.972 -766.02
## + log_pseudocalanus.sp.n 1 0.00010 35.065 -765.12
##
## Step: AIC=-784.93
## fish_cond ~ log_pseudocalanus.sp.c
##
## Df Sum of Sq RSS AIC
## + log_other.copepodite.and.n 1 0.44052 32.634 -787.48
## + log_egg 1 0.39373 32.681 -786.99
## + log_pseudocalanus.sp.n 1 0.28064 32.794 -785.82
## <none> 33.075 -784.93
## + log_other.calanoid.sp.c 1 0.10926 32.965 -784.05
## + log_cyclopoidae.sp.c 1 0.02944 33.045 -783.23
## + log_appendicularia 1 0.02773 33.047 -783.22
## + log_calanus.glacialis.c 1 0.02617 33.048 -783.20
## + log_other.calanus.sp.c 1 0.01109 33.064 -783.05
## + log_other 1 0.00402 33.071 -782.97
## + log_calanus.sp.n 1 0.00004 33.075 -782.93
## - log_pseudocalanus.sp.c 1 1.99037 35.065 -767.12
##
## Step: AIC=-787.48
## fish_cond ~ log_pseudocalanus.sp.c + log_other.copepodite.and.n
##
## Df Sum of Sq RSS AIC
## + log_egg 1 0.39690 32.237 -789.63
## <none> 32.634 -787.48
## + log_cyclopoidae.sp.c 1 0.14460 32.490 -786.98
## + log_other.calanoid.sp.c 1 0.11721 32.517 -786.70
## + log_pseudocalanus.sp.n 1 0.10234 32.532 -786.54
## + log_appendicularia 1 0.06153 32.573 -786.12
## + log_calanus.glacialis.c 1 0.03966 32.594 -785.89
## + log_calanus.sp.n 1 0.03739 32.597 -785.87
## + log_other.calanus.sp.c 1 0.01145 32.623 -785.60
## + log_other 1 0.00180 32.632 -785.50
## - log_other.copepodite.and.n 1 0.44052 33.075 -784.93
## - log_pseudocalanus.sp.c 1 2.25872 34.893 -766.79
##
## Step: AIC=-789.63
## fish_cond ~ log_pseudocalanus.sp.c + log_other.copepodite.and.n +
## log_egg
##
## Df Sum of Sq RSS AIC
## <none> 32.237 -789.63
## + log_other.calanoid.sp.c 1 0.11050 32.127 -788.79
## + log_pseudocalanus.sp.n 1 0.10441 32.133 -788.73
## + log_cyclopoidae.sp.c 1 0.06236 32.175 -788.28
## + log_other 1 0.03175 32.205 -787.96
## + log_appendicularia 1 0.03092 32.206 -787.95
## + log_calanus.sp.n 1 0.02225 32.215 -787.86
## + log_calanus.glacialis.c 1 0.01751 32.220 -787.81
## + log_other.calanus.sp.c 1 0.00029 32.237 -787.63
## - log_egg 1 0.39690 32.634 -787.48
## - log_other.copepodite.and.n 1 0.44368 32.681 -786.99
## - log_pseudocalanus.sp.c 1 1.62159 33.859 -774.99##
## Call:
## lm(formula = fish_cond ~ log_pseudocalanus.sp.c + log_other.copepodite.and.n +
## log_egg, data = prey_matrix_comb2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.98196 -0.20617 -0.01633 0.18031 1.16547
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.06808 0.03142 -2.167 0.0310 *
## log_pseudocalanus.sp.c 0.13805 0.03363 4.105 5.08e-05 ***
## log_other.copepodite.and.n -0.09181 0.04276 -2.147 0.0325 *
## log_egg 0.06022 0.02965 2.031 0.0431 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3102 on 335 degrees of freedom
## Multiple R-squared: 0.08064, Adjusted R-squared: 0.07241
## F-statistic: 9.795 on 3 and 335 DF, p-value: 3.283e-06## log_pseudocalanus.sp.c log_other.copepodite.and.n
## 1.112760 1.029607
## log_egg
## 1.083558
Contrairement au succès alimentaire, les caractéristiques taxonomiques des proies n’expliquent PAS bien la variabilité de l’indice de condition des poissons (\(R^2\) = 0.0724109).
Ceci est probablement dû au fait que la condition est une mesure intégratrice des conditions de vie rencontrée par l’individu.
On va maintenant vérifier avec des modèles mixtes l’influence possible de l’hétérogénéité régionale, bien que ce ne soit pas très intéressant…
## boundary (singular) fit: see ?isSingular## Warning: Model failed to converge with 1 negative eigenvalue: -3.7e+00## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula:
## fish_cond ~ log_egg + log_other.copepodite.and.n + log_pseudocalanus.sp.c +
## (log_egg + log_other.copepodite.and.n + log_pseudocalanus.sp.c |
## region)
## Data: prey_matrix_comb2
##
## REML criterion at convergence: 165
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.1617 -0.5907 -0.0142 0.5687 3.9776
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## region (Intercept) 0.018478 0.13594
## log_egg 0.002761 0.05255 -1.00
## log_other.copepodite.and.n 0.001729 0.04158 0.26 -0.26
## log_pseudocalanus.sp.c 0.009279 0.09633 0.17 -0.17 1.00
## Residual 0.085187 0.29187
## Number of obs: 339, groups: region, 9
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -0.04233 0.05745 5.42955 -0.737 0.492
## log_egg 0.04630 0.03496 9.72835 1.324 0.216
## log_other.copepodite.and.n -0.07869 0.04462 21.47810 -1.764 0.092 .
## log_pseudocalanus.sp.c 0.07258 0.04944 5.31989 1.468 0.199
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) log_gg lg_...
## log_egg -0.676
## lg_thr.cp.. -0.197 -0.043
## lg_psdcln.. -0.058 -0.188 0.144
## convergence code: 0
## boundary (singular) fit: see ?isSingular## Warning: Can't compute random effect variances. Some variance components equal zero. Your model may suffer from singulariy.
## Solution: Respecify random structure!
## You may also decrease the 'tolerance' level to enforce the calculation of random effect variances.## [1] NA## boundary (singular) fit: see ?isSingular
## boundary (singular) fit: see ?isSingular## Warning: Model failed to converge with 1 negative eigenvalue: -9.6e-03## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.00855504 (tol = 0.002, component 1)## ANOVA-like table for random-effects: Single term deletions
##
## Model:
## fish_cond ~ log_egg + log_other.copepodite.and.n + log_pseudocalanus.sp.c + (log_egg + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region)
## npar
## <none> 15
## log_egg in (log_egg + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 11
## log_other.copepodite.and.n in (log_egg + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 11
## log_pseudocalanus.sp.c in (log_egg + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 11
## logLik
## <none> -82.489
## log_egg in (log_egg + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) -83.445
## log_other.copepodite.and.n in (log_egg + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) -82.734
## log_pseudocalanus.sp.c in (log_egg + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) -83.612
## AIC
## <none> 194.98
## log_egg in (log_egg + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 188.89
## log_other.copepodite.and.n in (log_egg + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 187.47
## log_pseudocalanus.sp.c in (log_egg + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 189.22
## LRT
## <none>
## log_egg in (log_egg + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 1.91189
## log_other.copepodite.and.n in (log_egg + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 0.48973
## log_pseudocalanus.sp.c in (log_egg + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 2.24584
## Df
## <none>
## log_egg in (log_egg + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 4
## log_other.copepodite.and.n in (log_egg + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 4
## log_pseudocalanus.sp.c in (log_egg + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 4
## Pr(>Chisq)
## <none>
## log_egg in (log_egg + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 0.7520
## log_other.copepodite.and.n in (log_egg + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 0.9745
## log_pseudocalanus.sp.c in (log_egg + log_other.copepodite.and.n + log_pseudocalanus.sp.c | region) 0.6906## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula:
## fish_cond ~ log_egg + log_other.copepodite.and.n + log_pseudocalanus.sp.c +
## (1 | region)
## Data: prey_matrix_comb2
##
## REML criterion at convergence: 169.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.1962 -0.6185 0.0005 0.5414 3.9048
##
## Random effects:
## Groups Name Variance Std.Dev.
## region (Intercept) 0.01508 0.1228
## Residual 0.08792 0.2965
## Number of obs: 339, groups: region, 9
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -0.04239 0.05369 10.82426 -0.790 0.4468
## log_egg 0.05164 0.02936 333.99232 1.759 0.0796 .
## log_other.copepodite.and.n -0.07328 0.04251 333.02356 -1.724 0.0857 .
## log_pseudocalanus.sp.c 0.08518 0.03555 320.16780 2.396 0.0172 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) log_gg lg_...
## log_egg -0.316
## lg_thr.cp.. -0.292 -0.029
## lg_psdcln.. -0.221 -0.198 -0.123## # Intraclass Correlation Coefficient
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## Adjusted ICC: 0.146
## Conditional ICC: 0.141## [[1]]## `geom_smooth()` using formula 'y ~ x'
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## [[2]]$region## `geom_smooth()` using formula 'y ~ x'
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## [[4]]## `geom_smooth()` using formula 'y ~ x'
Ajouter les régions comme effet aléatoire n’apporte aucune information supplémentaire pour comprendre la variabilité de l’indice de condition des poissons.